1. Field of the Invention
The present invention is generally pertinent to a method for determining a storage capacity of a volume holographic material including photorefractive crystals and photopolymers and, more particularly, to a method for precisely determining a saturated photorefractive index and a recording time constant for transmission gratings of volume holographic material, and hence determining a dynamic range of the material. The storage capacity is proportional to the dynamic range; therefore, the dynamic range is an indicator for storage capacity.
2. Description of the Background
The volume holographic memory constructed by using photorefractive crystals, photopolymers, etc. is known to be an efficient approach for high capacity data storage and retrieval. The storage capacity is related to the dynamic range (M/#) of the material, which is proportional to the ratio of the saturated photorefractive index to the recording time constant (or half-growth time) τr. In an approach, measurement of the storage capacity is accomplished by computing the slope from the temporal trace of the square root of diffraction efficiency near the onset of recording. This approach is based on a result from the Coupled Wave Theory, which describes the diffraction efficiency as a function of time according to
  η  =            sin      2        ⁢                  π        ⁢                                  ⁢        Δ        ⁢                                  ⁢                              n            sat                    ⁡                      (                          1              -                              ⅇ                                                      -                    t                                    /                                      τ                    r                                                                        )                          ⁢        L                    λ        ⁢                                  ⁢        cos        ⁢                                  ⁢        θ            where Δnsat is the saturated photorefractive index (in the case of photopolymer it will be light-induced saturated incremental index), θ is the Bragg angle, L is the interaction length, and λ is the wavelength of the incident light. When the argument of the sine function is very small (which will occur if the ratio t/τr is sufficiently small), the slope of the temporal trace of the square root of diffraction efficiency will yield the ratio of the saturated photorefractive index to the recording time constant. However, without the knowledge of the recording time constant, one cannot make a proper choice of the time limit for the temporal trace to end. An improper choice of this time limit can amount to a 15% error of this value. The prior art have reported several ways to quantify the saturated photorefractive index of the reflection grating and the transmission grating in LiNbO3 but not the recording time constant measurement.
There are at least three techniques reported in the literature for such a measurement. The first technique uses optical path compensation (referred to as the null method) for measuring the birefringence change and hence the space charge field. During the course of the experiment, it takes a certain amount of time to establish the null measurement in order to collect each data point. Therefore, this technique is not a real-time measurement. This method is typically used to measure the change of the photorefractive index of the size of a laser spot inside the photorefractive crystal. It is impossible to use this method to measure the change of the photorefractive index of a region of an interference fringe (whose cross section is on the order of μm). Furthermore, this method requires using apparently identical two photorefractive crystals, and the precision is questionable due to the uncertainty of the equivalence of the photorefractive crystals.
The second technique uses a third beam as a probe to measure the diffraction efficiency from the refractive index grating. This technique requires knowledge of the interaction length, which in most calculations is usually approximated by the photorefractive crystal thickness. This technique, as employed in the prior art, measures the dynamic range (M/#) by using the method described in line 20 to line 23 in page 1, and therefore can not precisely measure the interaction length, the saturated photorefractive index, and the recording time constant as opposed to what is being disclosed in this invention. The third technique measures the energy transfer between beams from a two-beam coupling experiment. It requires a measurement of the relative phase shift in order to complete the calculation of the coupling coefficient, and hence the index amplitude of the grating at any given moment. This technique is less direct than the two previous methods and can't measure the saturated photorefractive index.
Thus there exists a need for a method to more precisely determine the dynamic range of volume holographic memories.